Monday, April 30, 2018

Carl Friedrich Gauss

Today's Google doodle is of Johann Carl Friedrich Gauß a.k.a. Carl Friedrich Gauss on the 241st anniversary of his birth, who is best known for his contributions to mathematics and physics.

He lived from 1777 to 1855, yet he is still a "household name". His name is the source of the term "Gaussian" to refer to a "normal" distribution in statistics; he was the first to prove the fundamental theorem of algebra; his gravitational constant, k, which is the positive square root of Newton's constant G, was still in use as an official physical constant until 2012 at very nearly the value he determined for it; and his calculations were used to rediscover dwarf planet Ceres.

The year 1796 [when he was 19 years old] was most productive for both Gauss and number theory. He discovered a construction of the heptadecagon on 30 March. He further advanced modular arithmetic, greatly simplifying manipulations in number theory. On 8 April he became the first to prove the quadratic reciprocity law. This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. The prime number theorem, conjectured on 31 May, gives a good understanding of how the prime numbers are distributed among the integers.

Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on 10 July and then jotted down in his diary the note: "ΕΥΡΗΚΑ! num = Δ + Δ' + Δ". On 1 October he published a result on the number of solutions of polynomials with coefficients in finite fields, which 150 years later led to the Weil conjectures.

He was a monarchist and a faithful Lutheran who never lived to see Germany as a unified country. He spent most of his life as an royal astronomer.

His first wife and love of his life life died in connection with the birth of their third child who died as an infant. Shortly thereafter, he married his late wife's best friend and they had three more children over the next twenty years after which she died, but he spent his entire life after the death of his first wife and his infant child in mourning.

He was one of the great mathematical geniuses of all time, but deliberately concealed from the world the methods by which he reached his final crystalized conclusions and declined to publish a large share of his findings and discoveries which he felt were inferior to his greatest accomplishments. He had few students, but was a mentor to Bernhard Riemann, whose non-Euclidian geometry was pivotal to the formulation of General Relativity, and a correspondent of Bessel (after whom "Bessel functions" are named) for whom he secured an honorary degree.